We address the solution of convex constrained nonlinear systems by new linesearch Quasi-Newton methods. These methods are based on a proper use of the projection map onto the constraint set and on a derivative-free and nonmonotone linesearch strategy. The convergence properties of the proposed methods are presented along with a worst-case iteration complexity bound. Several implementations of the proposed scheme are discussed and validated on bound-constrained problems including gas distribution network models. The results reported show that the new methods are very efficient and competitive with an existing affine-scaling procedure.
L. Marini, B. Morini, M. Porcelli, Quasi-Newton methods for constrained nonlinear systems: complexity analysis and application , Computational Optimization and Applications, 72:1 (2018), pp. 147-170. https://doi.org/10.1007/s10589-018-9980-7